Question

a. create a frequency table with 5-10 categories of equal width.b. Show the frequency histogram.c. Describe the shape of the distribution.d. Calculate the mean, median, and mode.e. Calculate the midrange.

Answer 1

Based on the photo, here are the data with its corresponding frequency:

17 - 1

19 - 1

21 - 1

22 - 2

23 - 1

26 - 1

29 - 1

30 - 2

31 - 2

32 - 4

34 - 2

41 - 2

42 - 1

44 - 3

45 - 1

In total, there are 26 data here.

To determine the class width, let's solve for the range first. The range is the difference between the maximum and the minimum data. The max data is 45 while the min data is 17. Therefore, the range is 45 - 17 = 28.

The next step is to divide the range by the number of classes we want to have. Since we have more than 20 data, the rule of thumb is to have 10 classes.

So, 28 divide by 10 = 2.8 ≈ 3. Our width will be 3.

Let's start the frequency table now.

Classes → Frequency

17 - 19 → 2

20 - 22 → 3

23 - 25 → 1

26 - 28 → 1

29 - 31 → 5

32 - 34 → 6

35 - 37 → 0

38 - 40 → 0

41 - 43 → 3

44 - 46 → 4

The frequency histogram for this table is shown below:

As shown above, the shape of the distribution is symmetric because the mean, mode, and median of the distribution is 32 and is found at the center of the distribution.

To solve for mean, add all the values given and then divide by 25.

The mean is 31.92, when rounded off, it is 32.

The mode is the data that has the highest frequency. Based on the data, 32 has a frequency if 4 and is the highest among all the data, therefore, 32 is the mode.

The median is the middlemost data when arranged from lowest to highest or vice versa. Out of the 25 values, the middle is the 13th. Based on the table, the 13th value is 32, therefore, the median is 32.

The midrange is (45 + 17)/2 = 62/2 = 31.