Question

Provided set of data are concentrations of suspended solids in river water that are collected for environmental characteristics. Total of 36 samples have concentrations of: 84 49 61 40 83 67 45 66 70 69 80 58 68 60 67 72 73 70 57 63 70 78 52 67 53 67 75 61 70 81 76 79 75 76 58 31

a) Construct a stem‐and‐leaf display of the data.

b) Calculate first and third quartiles and median from stem‐and‐leaf display

c) Construct histogram.

d) Construct box diagram.

e) Comment on the distribution of the data.

Answer 1

a) Construct a stem‐and‐leaf display of the data.

The stemplot is obtained in excel by following these steps,

Step 1: Write the data values in excel.

Step 2: Sort the data values by following below step,

Select the data values then DATA > Sort > OK. then Select Sort by: Treatment, Sort On: Values, Order: Smallest to Largest.

Step 3: Make a stem by taking the 10s digit of the data values as shown below,

Stem

3

4

5

6

7

8

Step 4: Write the unit digit values in from of the corresponding 10s digit.

(such that 3 | 1 represents 31 and 8 | 4 represents 84)

b)

First Quartile

From the stem plot,

Median value

From the stem plot,

Third quartile,

From the stem plot,

c)

Let the number of classes = 6

The histogram is obtained by counting the frequency within each class.

Classes	frequency
30-40	2
40-50	2
50-60	6
60-70	14
70-80	9
80-90	3

To plot a histogram in excel,

Step 1: write the data values in excel.

Step 2: Go to the chart area thane INSERT > Recommended Chart > Clustered Column. The screenshot is shown below,

d)

From part a and b, the five point summary is,

minimum value = 31

Q1 = 59.5

median = 67.5

Q3 = 75

maximum value = 84

The box plot using the five point summary is shown below,

e)

From the histogram, stem plot we can see that the distribution is slightly skewed to the left (longer tail in left)