Mean, Median, Mode, and Range: Additional Practice (Set 1)

Add the four values and divide by $4$.

$\text{mean} = \frac{14 + 18 + 22 + 26}{4} = \frac{80}{4} = 20$

Subtract the smallest value from the largest. The largest is $50$ and the smallest is $12$.

$\text{range} = 50 - 12 = 38$

Count each value: $13$ appears three times, $15$ appears twice, and $17$ once. The single most frequent value is the mode.

$\text{mode} = 13$

Add the five values and divide by $5$.

$\text{mean} = \frac{9 + 11 + 4 + 7 + 4}{5} = \frac{35}{5} = 7$

The sum is the mean times the number of values.

$\text{sum} = 6 \times 13 = 78$

The five numbers must add to $5 \times 30 = 150$. Subtract the four you know.

$150 - (28 + 35 + 22 + 40) = 150 - 125 = 25$

Count each value: $9$ appears three times, more than any other value.

$\text{mode} = 9$

The four scores must add to $4 \times 85 = 340$. Subtract the three known scores.

$340 - (88 + 92 + 79) = 340 - 259 = 81$

With four sorted values the median is the average of the second and third values, $x$ and $14$.

$\frac{x + 14}{2} = 11 \;\Rightarrow\; x + 14 = 22 \;\Rightarrow\; x = 8$

The current mean is $\frac{28}{4} = 7$. Adding a value equal to the mean leaves the mean unchanged.

$\frac{28 + 7}{5} = \frac{35}{5} = 7$

The mean is $\frac{28}{6} \approx 4.67$, the median is $\frac{4 + 4}{2} = 4$, and the mode is $4$.

$\text{mean} \approx 4.67 > \text{median} = \text{mode} = 4$

The six numbers add to $6 \times 10 = 60$. Removing $4$ leaves a sum of $56$ over $5$ values.

$\text{new mean} = \frac{60 - 4}{5} = \frac{56}{5} = 11.2$