Question

the following data set is given: 122, 130, 145, 154, 165, 178

adding which number to the set will increase its mean?

140
148
149
150

Explanation:

Calculate the sum of the data set

Find the sum of the given numbers.

$$ \text{Sum} = 122 + 130 + 145 + 154 + 165 + 178 = 894 $$

Find the current mean

Divide the sum by the number of values.

$$ \text{Mean} = \frac{894}{6} = 149 $$

Determine condition to increase mean

Adding a number greater than the mean increases it.

$$ x > 149 $$

Compare options with the mean

Evaluate the given choices against the mean.

$$ 150 > 149 $$

Answer:

• 140
• 148
• 149
• 150 (Correct answer)