Let's solve both parts step by step.

Part (a) Mean Calculation

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

Given dataLet's solve both parts step by step.

Part (a) Mean Calculation

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

Given
$13, 14, 14, 16, 16, 16, 16, 18, 18, 19$

First, sum the values: $13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19 = 160$

Now, count the number of values: There are 10 values.

Finally, calculate the mean: $\text{Mean} = \frac{160}{10} = 16 \text{ centimeters}$

Part (b) Mean Absolute Deviation (MAD) Calculation

The Mean Absolute Deviation (MAD) is the average of the absolute differences between each data value and the mean.

1. Calculate the differences from the mean (16): $|13 - 16| = 3, \quad |14 - 16| = 2, \quad |14 - 16| = 2, \quad |16 - 16| = 0, \quad |16 - 16| = 0$ $|16 - 16| = 0, \quad |16 - 16| = 0, \quad |18 - 16| = 2, \quad |18 - 16| = 2, \quad |19 - 16| = 3$

2. Sum these absolute differences: $3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3 = 14$

3. Divide by the number of values to get the MAD: $\text{MAD} = \frac{14}{10} = 1.4 \text{ centimeters}$

Final Answers:

a. Mean: $16$ centimeters
b. MAD: $1.4$ centimeters

Would you like more details on any of these calculations, or do you have any questions?

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Here are 5 related questions:

1. How would the mean change if a value of 20 was added to the data set?
2. What is the median of this data set?
3. How does the MAD help in understanding data variability?
4. What is the range of this data set?
5. How would the MAD change if all values were increased by 5?

Tip: The MAD is a useful measure to understand how spread out the values in a data set are from the mean.