Data Collection / Display

Data Collection / Display

Introduction
In your community, people collect data for different uses; for example, a class teacher records the number of learners present on a particular day, a headteacher records the number of teachers, support staff and learners in a school, health offcials collect data about patients’ well-being, among other uses. Quite often, you will also need to collect and display data. This topic will improve your understanding of data
collection and representation of different sorts of data.

3.1 Understanding Mode, Mean and Median as Measures of Location/Central Tendency and Knowing how to Find Them and when to Use Them
The measures of central tendency are the representative values for a given set ofdata. These include the mean, mode, and median. In this subtopic, you will understand
the measures of central tendency, know how to find and when to use them.
Understanding and finding mode as a measure of location/central tendency Activity 3.1 (a) (Work in groups)

(a) Discuss the staple food of the following tribes in Uganda.
Acholi
Karamojong Bagisu
Bakiga
Bakonjo
Sabiny
Lugbara
Banyankore Basoga
Baganda
Iteso
(c) Determine the most popular staple food among the tribes listed above.
(d) Mention the regions where each of the tribes listed in (a) are located in Uganda.
Understanding and finding mean and median as measures of location / central tendency
Activity 3.1 (b) (Work in arounds)

(a) Measure the lengths of the shirt sleeves of each member in your group.
(b) Record the lengths of the shirt sleeves.
(c) Find the average length of the shirt sleeves.
(d) Determine the middle number(s) of the lengths recorded in (b).
(e) Comment on your results.
When to use •mode’, •mean’ and •median’
As a consumer of information, it is important that you make decisions about which
measures of central tendency are most useful. Just because you can use mean, median
and mode in the real world does not mean that each measure applies to any situation.
Activity 3.1 (c) (Work in groups)
(a) Discuss the applications of mode, mean, and median in real-life situations.
(b) Compare the advantages and disadvantages of using mode, median and mean in different contexts.
(c) Present your findings to the rest of the class.

3.2 Understanding Range as a Measure of Dispersion/Spread and How to Find it
Knowing the average of a data set is not enough to describe the data set entirely For example, even when a sandal store owner knows that the average size of a man’s sandal is 8, he or she may not earn as much profit if only 8-sized sandals are stocked. This is because there could be potential customers who need sandals -of sizes greater or less than 8. This spread of size can be used to find the range.
Activity 3.2(a) (Work in groups)
Suggested materials: tape measure / string, metre rule Instructions:
(a) Stand in a circle while following your height order.
(b) Use the difference between the shortest and tallest member in your group to • determine the range of heights in your group.

3.3 Drawing and Using Frequency Tables for Ungroup Data
Ungrouped data are the data which you gather from an experiment or study, b
you do not sort them into categories, classes or groups.
After the collection phase, it is very important to present data in a meaningful way,
for the purposes of analyzing and making conclusions. One of the tools used to
present data is the frequency distribution table.
Drawing frequency tables for ungrouped data
A frequency distribution table is a table that keeps track of how many times something happens.
Activity 3.3(a) (Work in groups)
Suggested materials:

• adie
• recording materials
  Instructions:
  (a) Toss a die.
  (b) Read the number obtained on top and record it.
  (c) Repeat procedures (a)_(b) 19 times.
  .(d) Tabulate your results in an appropriate frequency table.
  (e) Use the results to determine the mean, median, modal values, and the range—
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3.4 Drawing and Using Frequency Tables for Grouped Data
In the previous subtopic, you were introduced to drawing and using frequency tables for ungrouped data sets; the same skills will be used here. But why should some data be grouped?
Activity 3.4 (Work in groups)
Suggested materials:

• a box / basin containing folded small pieces of paper

Instructions:
(a) Pick 20 pieces of paper for your group from the pool of papers provided.
(b) Unfold the papers, read and record each number on them.
(c) Draw a frequency table for the data generated, starting from 10—20, 20-30 etc. until your highest number acquires a group.
(d) Determine the class width / interval from your frequency table.
Note; Grouping data depends on the data given.

3.5 Estimating Measures of Location and Dispersion for Grouped Data
Just as discussed before, the measures of location / central tendency include the mode, mean, and median, while the range is a measure of dispersion. Measures of location for grouped data
Under this subsection, you will learn how to calculate the mode, mean, and median
for grouped data.
Calculating mean for grouped data
Earlier on, you learnt how to find the mean for ungrouped data.
Now, you will learn how to calculate mean for grouped data.
Activity 3.5(a) (Work in groups)
(a) i) Each member of a group is required to collect five dry leaves from the
surrounding environment.
ii) Put the leaves together and find their total number, in your group.
iii) Measure the length of each leaf.
iv) Record the results.
v) Draw a frequency distribution table for the results in (iv).
vi) Find the midpoint of each class.
vii) Find the product of each midpoint and the corresponding frequency.
viii) Obtain the total of the products.
ix) Find the ratio of the totals obtained in (viii) and (ii).
(d)What conclusion can you make about the outcome?

calculating mode for grouped mode

Earlier on, you learnt how to find the mode for ungrouped data. Now, you will learn
how to calculate mode for grouped data.
Activity 3.5(d) (Work in groups)
Using the frequency distribution table developed in Activity 3.5(b);
(a) Identify the lower class limit and the upper class limit for each class.
(b) Subtract the upper class limit of the first class from the lower class limit of
the second class.
(c) Divide the result in (b) by two.
(d) Subtract the result in (c) from the lower class limit of each class.
(e) Add the result in (c) to the upper class limit of each class.
(f) Tabulate your results and make a conclusion.
Activity 3.5(e) (Work in groups)
(a) Use the frequency distribution table you developed in Activity 3.5(a) to determine the;
i) modal class
ii) lower class boundary and class interval of the modal class
iii) differences between the frequency of the modal class and that of the class; before it (d,) and after it (d)
iv) sum of the differences in (d, + d2)
v) ratio of the first difference in (iii) to the sum in (iv)
vi) product of your result in (v) and the class interval
vii) sum of the lower class boundary in (ii) and the product in (vi)
(b) What conclusion can you make about this outcome?

Calculating median for grouped data
Earlier on, you also learnt how to find the median of ungrouped data. Now, you will learn how to calculate median for grouped data.

ctivity 3.5(t) (Work in groups)
(a) Use the frequency distribution table you developed in Activity 3.5(a) to determine the;
i) median class
ii) lower class boundary of the median class and the class interval
iii) frequency of the median class
iv) cumulative frequency before that of the median class
v) difference between one half of the total frequency and the result in (iv)
vi) ratio of your result in (v) to the frequency of the median class in (iii)
vii) product of your result in (vi) and the class interval
viii) sum of the lower class boundary of the median class and the result in (vii)
(b) What conclusion can you make about this outcome?

Measures of dispersion for grouped data
Two data sets can have the same mean but be (the sets themselves) entirely different! Thus, to describe data, one needs to know the extent of variability This is given by the measures of dispersion for grouped data, among which is the interquartile range.

Calculating interquartile range
Activity 3.5(g) (Work in groups)
(a) Use the frequency distribution table you developed in Activity 3.5(a) to determine the;
i) lower quartile class
ii) lower class boundary of the lower quartile class and the class interval
iii) frequency of the lower quartile class
iv) cumulative frequency before that of the lower quartile class
v) difference between one quarter of the total frequency and the result in (iv)
vi) ratio of your result in (v) to the frequency of the lower quartile class in (iii)
vii) product of your result in (vi) and the class interval
viii) sum of the lower class boundary of the lower quartile class and the result
in (vii)
(b) Make a conclusion about this outcome.

Activity 3.5(h) (Work in groups)
(a) Use the frequency distribution table you developed in Activity 3.5(a) to determine the;
i) upper quartile class
ii) lower class boundary of the upper quartile class and the class interval
iii) frequency of the upper quartile class
iv) cumulative frequency before that of the upper quartile class
v) difference between three quarters of the total frequency and result in (iv)
vi) ratio of your result in (v) to the frequency of the upper quartile class in (iii)
vii) product of your result in (vi) and the class interval
viii) sum of the lower class boundary of the upper quartile class and the result
in (vii)
(b) Make a conclusion about this outcome.
i) Determine the difference between your result in Activity 3.5(h) part (viii)
and that in Activity 3.5(g) part (viii).
(c) What do you conclude about this outcome?

3.6 Drawing a Histogram with Equal Class Intervals and Using it to Estimate the Mode
In Senior One, you drew bar charts. Now, under this subtopic, you will draw and use
histograms to estimate mode.
Activity 3.6 (Work in groups)
The table below shows the masses of learners who turned up for safe male circumcision at matany hospital

(a) Draw a frequency distribution table for the data above.
(b) Draw a graph of frequencies against lower class boundaries.
(c) Identify the highest bar on your graph and use it to estimate the mode.
(d) Explain how you estimated the mode using the graph.
(e) Present your results to the rest of the class.

ICT Activity
In groups:
(a) Choose a topic for data collection.
(b) Collect data on the topic in (a) above.
(c) Use a frequency table to organise your data.
(d) Use a spreadsheet program to display your data on a;
i) cumulative frequency curve
ii) histogram

f’ Revision Questions:
1) The times, in minutes, that some people spend talking on phone in one day
are shown below,
30 40 35 32 62 73 94 81 80 79 30 40 62 80 32
35 30 40 32 79 79 94 62 79 62 73
35 73 94 81
(a) Draw a frequency table for the above data, starting with the class 30-39.
(b) Calculate the mean time.
(c) Draw a histogram and use it to estimate the modal time.
(d) Draw an ogive and use it to estimate the median time.
2) The table below shows the lengths of beds in the dormitory of a certain school.

(a) Draw a histogram and use it to estimate the modal length.
(b) Draw a cumulative frequency curve and use it to estimate the median length.
The data below are of the weights of patients in a certain health unit.

Draw an ogive and use it to estimate the median and interquartile range.

Vectors