# Histograms, Frequency Polygons, Mean, Median, Mode, Class Mid-Point, Pie and Bar Charts

Q1. The masses of 50 similar castings are measured correct to the nearest 0.1 kg, and the results are shown below.

8.1 7.7 7.4 8.6 7.8 8.1 8.6 8.0 7.3 9.0

9.0 7.3 8.5 7.7 8.3 7.9 7.5 8.1 7.1 7.8

9.1 7.6 8.2 8.4 8.5 9.0 7.8 7.6 8.4 7.7

8.2 9.0 7.2 8.3 7.4 8.1 8.3 8,5 8.7 7.9

7.5 8.9 7.7 7.1 8.2 9.1 7.1 8.8 8.0 8.8

(a) From these results reproduce and fill out the table below

Class Class mid-point (x) Frequency(f) f.x

7.1 to 7.3

7.4 to 7.6

7.7 to 7.9

8.Oto8.2

8.3 to 8.5

8.6 to 8.8

8.9 to 9.1

(b) Draw the frequency polygon for the data.

(c) Draw the histogram for the data.

(d) Calculate:

(1) the mean (ii) the mode (iii) the median

All calculations must be shown and the graphs must be hand drawn.

QI. In a certain university the number of students enrolled by the faculties is given

the table below:

Faculty Number of

students

Business and administration 1950

Humanities and social science 2820

Physical and life sciences 1050

Technology 850

Total 6670

Manipulate the data above to produce:

(a) A pie chart.

(b) A bar chart.

Q2. The data below show the average temperature in °C for each month as indicated.

Month Jan March May July Sept bec

Temperature °C 4.5 8.1 15 21.8 17.2 3.8

Manipulate the above data to produce:

(a) A graph of temperature against month for the year.

(b) Use the graph to estimate the average temperature for the month of June.

(c) Use the graph to estimate the average temperature for the month of November.

The graph must be hand drawn with the estimated temperature for (b) and (c) clearly indicated on it.

#### Solution Preview

Please see the attached file for the complete solution (answers are on different sheets in the same file).

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Q1: the question on measurements of 50 castings

The mid-points are easily enough to determine.

For Class 7.1 to 7.3, the midpoint is 7.2.

For Class 7.4 to 7.6, the midpoint is 7.5.

The rest you can determine. It's just the half way point between the two numbers. To calculate it, you add up the two numbers and divide by 2. For example, for the first class, 7.1 + 7.3 = 14.4. Then divide by 2 = 7.2

To determine frequency, you must count the number of measurements that fall within each class. For example, for Class 7.1 to 7.3, the frequency is 6. There are six measurements that fall within the interval, 7.1 to 7.3.

Also, for Class 7.4 to 7.6, the frequency is also 6.

The rest you can determine. Just count up the number of measurements that fall within the limits of each class.

The last column of the table, you must multiply the mid-point (x) by the frequency (f). Therefore, for the first class, you would have 7.2 x 6 = 43.2.

For the second class, the 7.4 to 7.6 class, you calculate f.x as, 7.5 x 6 = 45.

You can repeat those ...

#### Solution Summary

Histograms, Frequency Polygons, Mean, Median, Mode, Class Mid-Point, Pie and Bar Charts are investigated.