Question

construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. describe any patterns. number of classes: 8 data set: finishing times (in seconds) of 20 male participants in a 5k race 1716 1635 1570 1475 2296 1444 1251 1801 1594 1779 1959 1522 1825 1617 1303 1818 2019 2083 1582 1479 construct a frequency distribution of the data. use the minimum data entry as the lower limit of the first class. class frequency 1. 1303 - 2. - 3. - 4. - 5. - 6. - 7. - 8. -

Explanation:

Step1: Find range

The maximum value in the data - set is 2296 and the minimum is 1251. Range = 2296 - 1251=1045.

Step2: Calculate class width

Class width = $\frac{\text{Range}}{\text{Number of classes}}=\frac{1045}{8}\approx130.625$. We round up to 131.

Step3: Define classes

1. First class: 1251 - 1381
2. Second class: 1382 - 1512
3. Third class: 1513 - 1643
4. Fourth class: 1644 - 1774
5. Fifth class: 1775 - 1905
6. Sixth class: 1906 - 2036
7. Seventh class: 2037 - 2167
8. Eighth class: 2168 - 2298

Step4: Count frequencies

1. For the class 1251 - 1381: Frequency = 1 (since only 1251 is in this range)
2. For the class 1382 - 1512: Frequency = 4 (1444, 1475, 1479, 1522)
3. For the class 1513 - 1643: Frequency = 5 (1570, 1582, 1594, 1617, 1635)
4. For the class 1644 - 1774: Frequency = 3 (1716, 1779)
5. For the class 1775 - 1905: Frequency = 2 (1801, 1818)
6. For the class 1906 - 2036: Frequency = 2 (1959, 2019)
7. For the class 2037 - 2167: Frequency = 1 (2083)
8. For the class 2168 - 2298: Frequency = 1 (2296)

Class	Frequency
1382 - 1512	4
1513 - 1643	5
1644 - 1774	3
1775 - 1905	2
1906 - 2036	2
2037 - 2167	1
2168 - 2298	1

Answer:

Class	Frequency
1382 - 1512	4
1513 - 1643	5
1644 - 1774	3
1775 - 1905	2
1906 - 2036	2
2037 - 2167	1
2168 - 2298	1