Question

Problem 4 (10 marks)

The number of calls received per week by the clients services of a cell phone company over the last 40 weeks are given as follows:

63 74 42 65 51 54 36 56 68 57 62 64 76 67 79 61 81 77 59 38 84 68 71 94 71 86 69 75 91 55 48 82 83 54 79 62 68 58 41 47

a) Prepare a frequency distribution (table) and histogram for the data. Specify the

number of bins, the width of the bins and the bins limits. (8 marks) b) Describe the histogram that you have obtained. Justify your answer. (2 marks)

Answer 1

We will use Microsoft Excel to draw the histogram.

First decide the number of bins.

For the data set of 40 numbers 6 bins will be sufficient. you can choose any number between 5 and 20 bins. Bigger data set required more number of bins.

now we have to find the range minimum value from maximum value.

Now to find the weight of the bin we divide the range by number of bins. (approximate to whole number)

Max Min Range Bin size 94 36 58 10

enter the data into Excel as mentioned below:

B C D E F I A 1 No. of Calls 2 63 Bin Max 35 74 Min 45 3 4 94 =MAX(A2:A41) 36 =MIN(A2:A41) 58 =D2-D3 10 =ROUND(D4/6,0) 42 55 Range Bin size 5 65 65 6 51 75 7 54 85 8 36 95 ON 56 10 68 11 57 12 62 13 64 14 76 15 67 16 79 17 61 18 81 19 77 20 59 21 38 22 84

Go to data tab and then to data analysis toolpak .

now select histogram

AutoSave Off H9 x x 2 = Book1 - Excel Mr. Mayank Dugar MM File Home Insert Page Layout Formulas Data Review View Help Search Share Comments OH Queries & Connections B Properties Edit Links 21 22 Y clear Data Analysis ? Solver e là Stocks Sort Get Data Geography = Outline Filter Refresh All- ZL. Text to Reapply Advanced Columns ES What If Forecast Analysis Sheet Forecast Get & Transform Data Queries & Connections Data Types Sort & Filter Data Tools Analyze E17 fac D E F Н T K 1 M N O P 0 R S Bin А 1 No. of Calls 2 63 3 74 35 ? x 45 Max Min Range Bin size 94 =MAX(A2:A41) 36 =MIN(A2:A41) 58 =D2-D3 10 =ROUND(D4/6,0) OK 4 42 55 65 65 Cancel 5 6 7 51 75 Data Analysis Analysis Tools Anova: Single Factor Anova: Two-Factor With Replication Anova: Two-Factor Without Replication Correlation Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram Help 54 85 8 36 95 9 56 10 68 11 57 12 62 13 64 14 76 15 67 16 79 17 61 18 81 77 59 19 20 21 22 38 84 Sheet1 + Ready 5 + 100% I Type here to search ORI E W х M D () / ENG 6:05 AM 01-Aug-20

Enter Values as shown below

? х Histogram Input Input Range: Bin Range: OK SA$1:$A$41 1 Cancel $F$1:$F58 Help Labels SH$1 1 Output options Output Range: New Worksheet Ply: O New Workbook Pareto (sorted histogram) Cumulative Percentage Chart Output

you will see a frequency table and histogram

к L M N P O ا H No of calls Frequency 35 0 Histogram 45 4 55 6 15 65 10 10 75 9 85 8 Frequency 95 3 56 More 0 More No of calls

Resize the histogram as required

Histogram 12 LO 00 Frequency 6 Frequency 4 2 0 35 45 55 65 75 85 95 More No of calls

Even increase the bar width by double-clicking the bars.

Describing the histogram.

The Distribution looks very close to normal distribution.

Maximum number of times 55 to 65 calls are received.

Receiving more than 85 calls and less than 45 calls is very less.

If it helps, kindly upvote.

Comment below for doubt.