Question

construct the cumulative - frequency distribution for the given data.
age (years) of best actress when award was won frequency
20 - 29 27
30 - 39 34
40 - 49 13
50 - 59 2
60 - 69 5
70 - 79 2
80 - 89 1
age (years) of best actress when award was won cumulative frequency
less than 30
less than 40
less than 50
less than 60
less than 70
less than 80
less than 90

Explanation:

Step1: Define cumulative frequency

Cumulative frequency is the running - total of frequencies.

Step2: Calculate cumulative frequency for less than 30

The frequency for ages 20 - 29 is 27. So, the cumulative frequency for less than 30 is 27.

Step3: Calculate cumulative frequency for less than 40

We add the frequency of ages 30 - 39 (34) to the previous cumulative frequency. $27+34 = 61$.

Step4: Calculate cumulative frequency for less than 50

We add the frequency of ages 40 - 49 (13) to the previous cumulative frequency. $61 + 13=74$.

Step5: Calculate cumulative frequency for less than 60

We add the frequency of ages 50 - 59 (2) to the previous cumulative frequency. $74+2 = 76$.

Step6: Calculate cumulative frequency for less than 70

We add the frequency of ages 60 - 69 (5) to the previous cumulative frequency. $76+5 = 81$.

Step7: Calculate cumulative frequency for less than 80

We add the frequency of ages 70 - 79 (2) to the previous cumulative frequency. $81+2 = 83$.

Step8: Calculate cumulative frequency for less than 90

We add the frequency of ages 80 - 89 (1) to the previous cumulative frequency. $83+1 = 84$.

Answer:

Less than 30: 27
Less than 40: 61
Less than 50: 74
Less than 60: 76
Less than 70: 81
Less than 80: 83
Less than 90: 84