Constructing a histogram

Explains how to create histogram

1. Constructing a Histogram Presented By: Tobby Gondwe

2. Introduction In this lesson, we will construct a histogram. Objective To construct a histogram from given data set.

3. Introduction There are many different ways to organize data, which later is used to construct Histograms. In this lesson, we will use the Five-Step approach. This approach is ideal when dealing with raw data.

4. Step One Count the number of data points given Suppose we have collected data on the test scores in science as shown here: 45 36 54 48 51 61 74 79 45 49 89 49 64 83 87 45 67 63 60 84 57 54 60 84 93 47 56 65 93 64 81 73 41 68 52 64 43 67 73 68 71 77 88 67 63 72 53 59 72 53 64 87 43 53 87 91 46 58 65 59 Simply counting the total number of entries in the above data set completes this step. In this example, there are 60 data points.

5. Step Two Summarize data on a tally sheet . You need to summarize your data to make it easy to interpret. You can do this by constructing a tally sheet. First, find the range of the scores: Range = Highest – lowest Range = 93 – 36 = 57 In simple terms, there are more than 57 individual scores to be written down. This is not possible. Hence, we use groups or classes or bins.

6. Step Two Continues Number of Bins = Bin width is 10 Number of bins = = 5.7 5.7 means that we will increase the number of bins to 6, starting with 35 to 44, 45 to 54,..  

7. Step Two continues Bin Tally Frequency 35 to 44 ///// 5 45 to 54 ///// ///// ///// 15 55 to 64 ///// ///// //// 14 65 to 74 ///// ///// /// 13 75 to 84 ///// // 7 85 to 94 ///// / 6 Total 60

8. Step Three Determine the bin boundaries Since each includes the limit values as seen from the table, we find the boundary by getting the upper bin limit of the preceding bin and the lower bin limit of the succeeding bin: For bin 35 to 44, it is 44 For bin 45 to 54, it is 45

9. Step Three We need to draw the X axis and the Y axis as shown below:

10. Step Three We complete the Histogram

11. Step Three The above Histogram is misleading. It shows as if there are no values between the classes or bins. The best way to do this is to create bin or class boundaries that will enable us include others values in the bars.

12. Step Three Continues Bin boundary = Bin boundary = = 44.5 This shows that each bin will have .5 boundary. Therefore, the boundaries are: 34.5, 44.5, 54.5, 64.5, 74.5, 84.5 and 94.5  

13. Step Four Determine the highest frequency value to be used. The highest frequency in the table is 16. we will use an interval of 2 units on the frequency axis. On the bin axis, we will use the bin boundaries in an equal interval of 1 unit.

14. Step Four Continues Draw the appropriate axes as shown below:

15. Step Five We complete the Histogram by drawing the bars according to the frequencies in the table. Bin (Class) Frequency 34.5 – 44.5 5 44.5 – 54.5 15 54.5 – 64.5 14 64.5 – 74.5 13 74.5 – 84.5 7 84.5 – 94.5 6

16. Step Five Continues Draw the Histogram

17. Conclusion This is how we can construct or create a histogram given a data set. Exercise Construct a histogram using the following data set. Weekly wage Frequency 15 – 19 8 20 - 24 10 25 - 29 16 30 - 34 25 35 - 39 14 40 - 44 7

18. The End! Thank you!