Using the table, calculate the median, mode, and mean shoe size of the girls.

Formula: $\bar{x} = \frac{\sum f_i x_i}{N}$

Compute $\sum f_i x_i$:

Substitute: $\bar{x} = \frac{164}{11}$

Mode is the value of $x_i$ with the highest frequency.
Highest $f_i = 4$ at $x_i = 14$.
Mode = 14

Cumulative frequency (cf) table:

$N=11$ (odd), median is the $\frac{N+1}{2} = 6$th observation.
$5 < 6 \leq 7$, so median $= 15$.
Median = 15

Section A: Mean = \dfrac{164}{11}, Median = 15, Mode = 14

Section B

Frequency distribution table:

Formula: $\bar{x} = \frac{\sum f_i x_i}{N}$

Compute $\sum f_i x_i$:

Substitute: $\bar{x} = \frac{130}{12} = \frac{65}{6}$

Mode is the value of $x_i$ with the highest frequency.
Highest $f_i = 6$ at $x_i = 10$.
Mode = 10

Cumulative frequency (cf) table:

$N=12$ (even), median is average of $\frac{N}{2}=6$th and $7$th observations.
$6$th: cf $6 \geq 6$, so 10.
$7$th: cf $6 < 7 \leq 9$, so 11.
Median $= \frac{10 + 11}{2} = 10.5 = \frac{21}{2}$.
Median = \dfrac{21}{2}

Section B: Mean = \dfrac{65}{6}, Median = \dfrac{21}{2}, Mode = 10

Section A: mean = 164/11, median = 15, mode = 14

Section B: mean = 65/6, median = 21/2, mode = 10