Following data shows the number of wickets taken by a player in last 11 matches played by him/her : 1, 0, 2, 4, 0, 3, 1, 1, 2, 4, 1
What is the difference between the mean and mode of the above data ?

Question

Following data shows the number of wickets taken by a player in last 11 matches played by him/her : 1, 0, 2, 4, 0, 3, 1, 1, 2, 4, 1 
What is the difference between the mean and mode of the above data ?

Accepted Answer

To determine the difference between the mean and mode of the given data set, we need to calculate both the mean and the mode of the data.

**Data Set:** 1, 0, 2, 4, 0, 3, 1, 1, 2, 4, 1

**Step 1: Calculate the Mean**

The mean is calculated by summing all the values and dividing by the number of values.

Sum of the data = 1 + 0 + 2 + 4 + 0 + 3 + 1 + 1 + 2 + 4 + 1 = 19

Number of matches = 11

Mean = Sum of the data / Number of matches = 19 / 11

Mean = $\frac{19}{11}$

**Step 2: Calculate the Mode**

The mode is the number that appears most frequently in the data set.

In the given data, the number 1 appears 4 times, which is more frequent than any other number.

Therefore, the mode is 1.

**Step 3: Calculate the Difference between Mean and Mode**

Difference = Mean - Mode

Difference = $\frac{19}{11}$ - 1

To subtract, convert 1 to a fraction with the same denominator:

1 = $\frac{11}{11}$

Difference = $\frac{19}{11}$ - $\frac{11}{11}$ = $\frac{19 - 11}{11}$ = $\frac{8}{11}$

Thus, the difference between the mean and the mode is $\frac{8}{11}$.

**Explanation of Options:**

1. **Option 1: $\frac{8}{9}$** - This option is incorrect because the calculated difference is $\frac{8}{11}$, not $\frac{8}{9}$.

2. **Option 2: $\frac{7}{11}$** - This option is incorrect because the calculated difference is $\frac{8}{11}$, not $\frac{7}{11}$.

3. **Option 3: $\frac{8}{11}$** - This is the correct option as it matches the calculated difference between the mean and the mode.

4. **Option 4: $\frac{10}{9}$** - This option is incorrect because the calculated difference is $\frac{8}{11}$, not $\frac{10}{9}$.

Therefore, the correct answer is Option 3: $\frac{8}{11}$.