A histogram shows the daily earnings of 100 workers. Use the histogram to answer the following questions: a) In which earning group are the maximum workers? b) What is the size of the classes? c) How

From the given histogram for daily earnings of 100 workers:

• 100-150 Rs: 30 workers
• 150-200 Rs: 40 workers
• 200-250 Rs: 15 workers
• 250-300 Rs: 10 workers
• 300-350 Rs: 5 workers

a) In which earning group are maximum workers?
The highest bar corresponds to the 150-200 Rs group with 40 workers.
The maximum number of workers are in the earning group $\boxed{\text{150-200 Rs}}$.

b) What is the size of the classes?
The class size is the difference between the upper and lower limits of any class interval. For example, for the 100-150 Rs class, the size is $150 - 100 = 50$.
The size of the classes is $\boxed{\text{50 Rs}}$.

c) How many workers are in the maximum earning group?
The maximum earning group is 300-350 Rs.
There are $\boxed{\text{5 workers}}$ in the maximum earning group.

d) How many workers earn less than ₹ 200?
This includes workers in the 100-150 Rs and 150-200 Rs groups.
Number of workers $= 30 + 40 = 70$.
$\boxed{\text{70 workers}}$ earn less than ₹ 200.

e) How many workers earn ₹ 200 or more?
This includes workers in the 200-250 Rs, 250-300 Rs, and 300-350 Rs groups.
Number of workers $= 15 + 10 + 5 = 30$.
$\boxed{\text{30 workers}}$ earn ₹ 200 or more.

From the given histogram for runs scored by a cricket player:

• 0-20 runs: 1 match
• 20-40 runs: 6 matches
• 40-60 runs: 9 matches
• 60-80 runs: 4 matches
• 80-100 runs: 2 matches

a) How many matches did he play in the highest runs group?
The highest runs group is 80-100 runs.
He played $\boxed{\text{2 matches}}$ in the highest runs group.

b) How many matches did he play?
Total number of matches $= 1 + 6 + 9 + 4 + 2 = 22$.
He played a total of $\boxed{\text{22 matches}}$.

c) In how many matches did he score 60 or more runs?
This includes matches in the 60-80 runs and 80-100 runs groups.
Number of matches $= 4 + 2 = 6$.
He scored 60 or more runs in $\boxed{\text{6 matches}}$.

d) In how many matches did he score less than 40 runs?
This includes matches in the 0-20 runs and 20-40 runs groups.
Number of matches $= 1 + 6 = 7$.
He scored less than 40 runs in $\boxed{\text{7 matches}}$.

To construct a histogram from the grouped frequency distribution table prepared in Q.4:
The table from Q.4 is:

$$\begin{array}{|c|c|} \hline \text{Height (in cm)} & \text{Frequency} \\ \hline 150-155 & 6 \\ 155-160 & 2 \\ 160-165 & 10 \\ 165-170 & 12 \\ 170-175 & 7 \\ 175-180 & 3 \\ \hline \end{array}$$

Follow these steps to draw the histogram:

• Draw a horizontal axis (x-axis) and label it "Height (in cm)". Mark intervals corresponding to the class intervals: 150-155, 155-160, 160-165, 165-170, 170-175, 175-180.
• Draw a vertical axis (y-axis) and label it "Frequency". Choose a suitable scale (e.g., 1 unit = 1 frequency).
• For each class interval, draw a rectangular bar whose width is equal to the class interval and whose height is proportional to its frequency. The bars should be adjacent to each other without any gaps.
  • For 150-155, draw a bar of height 6.
  • For 155-160, draw a bar of height 2.
  • For 160-165, draw a bar of height 10.
  • For 165-170, draw a bar of height 12.
  • For 170-175, draw a bar of height 7.
  • For 175-180, draw a bar of height 3.