Find the cummulative relative frequency for ages number of students

1. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.

2.A relative frequency is the fraction of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of students in the sample - in this case, 20. Relative frequencies can be written as fractions, percents, or decimals.

Twenty students were asked how many hours they worked per day. Their responses, in hours, are listed below, followed by a frequency table listing the different data values in ascending order and their frequencies.

5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3

Data Value Frequency

2 3

3 5

4 3

5 6

6 2

7 1

A frequency is the number of times a given datum occurs in a data set. According to the table above, there are three students who work 2 hours, five students who work 3 hours, etc.

The total of the frequency column, 20, represents the total number of students included in the sample.

A relative frequency is the fraction of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of students in the sample - in this case, 20. Relative frequencies can be written as fractions, percents, or decimals. Cumulative relative frequency is the accumulation of the previous relative frequencies.

To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

# Entering the data

hours.worked = c(5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6,

5, 4, 4, 3, 5, 2, 5, 3)

# A general frequency table

table(hours.worked)

## hours.worked

## 2 3 4 5 6 7

## 3 5 3 6 2 1

# Relative frequency table

table(hours.worked)/length(hours.worked)

## hours.worked

## 2 3 4 5 6 7

## 0.15 0.25 0.15 0.30 0.10 0.05

# To get cumulative frequencies, we need to put

# the hours into different intervals

x = table(cut(hours.worked, breaks = c(1:7)))

# Cumulative frequencies

cumsum(x)

## (1,2] (2,3] (3,4] (4,5] (5,6] (6,7]

## 3 8 11 17 19 20

# Cumulative relative frequencies

cumsum(x)/length(hours.worked)

## (1,2] (2,3] (3,4] (4,5] (5,6] (6,7]

## 0.15 0.40 0.55 0.85 0.95 1.00