The problem requires creating a histogram from the given data. The data consists of shift durations for each day of the week, and the histogram should group this data into bins of width 3 (0-3, 3-6, 6-9). The histogram must exclude the left endpoint and includes the right endpoint of the interval. The given data is: Monday: 2.0, 1.5 Tuesday: 1.8, 1.8 Wednesday: 1.8 Thursday: 1.1 Friday: 4.6, 4.0 Saturday: 4.0 Sunday: 7.5

1. Problem Description

The problem requires creating a histogram from the given data. The data consists of shift durations for each day of the week, and the histogram should group this data into bins of width 3 (0-3, 3-6, 6-9). The histogram must exclude the left endpoint and includes the right endpoint of the interval.

The given data is:

Monday: 2.0, 1.5

Tuesday: 1.8, 1.8

Wednesday: 1.8

Thursday: 1.1

Friday: 4.6, 4.0

Saturday: 4.0

Sunday: 7.5

2. Solution Steps

Step 1: Count the number of data points that fall within each bin.

Bin 1: (0, 3] - This bin includes values strictly greater than 0 and less than or equal to

3. - Monday: 2.0, 1.5 are in this bin.

- Tuesday: 1.8, 1.8 are in this bin.

- Wednesday: 1.8 is in this bin.

- Thursday: 1.1 is in this bin.

So, the number of data points in this bin is 2 + 2 + 1 + 1 =

6.

Bin 2: (3, 6] - This bin includes values strictly greater than 3 and less than or equal to

6. - Friday: 4.6, 4.0 are in this bin.

- Saturday: 4.0 is in this bin.

So, the number of data points in this bin is 2 + 1 =

3.

Bin 3: (6, 9] - This bin includes values strictly greater than 6 and less than or equal to

9. - Sunday: 7.5 is in this bin.

So, the number of data points in this bin is

1.

Step 2: Plot the histogram based on the count calculated in Step

1.

The bin (0, 3] has a height of

6. The bin (3, 6] has a height of

3. The bin (6, 9] has a height of

1.

3. Final Answer

The histogram should have bars with the following heights:

Bin (0, 3]: 6

Bin (3, 6]: 3

Bin (6, 9]: 1