You are given the following data on the ages of students in my micro class: {17,

Question

You are given the following data on the ages of students in my micro class: {17, 45, 33, 32, 38, 28, 27, 22, 26, 29, 40, 19, 18, 34, 33, 28, 27, 18, 19, 23} a. Construct a frequency and relative frequency distribution using the table below. b. Construct a frequency Histogram of the data. c. Comment on the shape of the distribution? Does the shape tell you anything? Explain. The Histogram above skewed right. Which means that there are fewer individuals in the Micro class above the age of 35 than below the age 35.

Explanation / Answer

FULL ANSWERS PROVIDED. ONLY EXPLANATION IS ASKED.

(a) Given the raw data:

16,45,33,33,32,38,28,27,22,26,29,40,19,18,34,33,28,27,18,19,23.

For drawing the frequency distribution:

Step 1: Maximum value = 45

Minimum value = 16

Step 2:

So, write down the class intervals as:

16 - 21

22-27

28-33

34-39

40-45.

Step 3:

Calculate the number of values in each class interval.

For example, we note: 16,19,18,18,19 are in the interval 16-21. So, frequency of class 16-21 is 5.

Similarly, frequency of class 22-27 is 5. Frequency of class 28-33 is 4.

Frequency of class 34-39 is 1

Frequency of class 40-45 is 2.

Thus, frequency distribution is written as:

class interval            frequency

16-21                         5

22-27                        5

28-33                        4

34-39                         1

40-45                          2

Step 4:

We note total frequency = 20.

Relative frequency is obtained by dividing the frequency of each class by 20 as follows:

class                   frequency             relative frequency

16-21                       5                          5/20 = 0.25

22-27                       5                          5/20 = 0.25

28-33                       4                         4/20=0.20

34-39                      1                             1/20=0.05

40-45                     2                               2/20=0.10

(b) Frequency histogram is drawn as follows:

Step 1:

Mark on the axis the class intervals: 16-21, 22-27, 28-33, 34-39, 40-45

Step 2:
Mark on the y axis: 0, 0.05,0.10, 0.15,0.20,0.25.

PLEASE NOTE THE MISTAKE IN THE GIVEN MARKING: The markings should be of equal interval: but, in the given graph, the marking 0.15 & 0.25 are not seen.

Step 3:

Against each class, mark the corresponding relative frequency.

Step 4:

Join the rectangle.

(c) EXPLANATION:

Skewed right means the hump of the curve is towards the left of the mid value. That means there are fewer values above 35 than below 35.

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