Question

estimate the mean number of classes taken by a high school student as displayed in the histogram.
(1 point)
the mean of the data set is 6 ×

Explanation:

Step1: Find mid - points

For 0 - 4.9: mid - point $m_1 = 2.45$; for 5 - 9.9: $m_2=7.45$; for 10 - 14.9: $m_3 = 12.45$; for 15 - 19.9: $m_4=17.45$; for 20 - 24.9: $m_5 = 22.45$.

Step2: Multiply mid - points by frequencies

$f_1 = 1$, $f_2 = 6$, $f_3 = 10$, $f_4 = 6$, $f_5 = 1$. So $m_1f_1=2.45\times1 = 2.45$, $m_2f_2=7.45\times6 = 44.7$, $m_3f_3=12.45\times10 = 124.5$, $m_4f_4=17.45\times6 = 104.7$, $m_5f_5=22.45\times1 = 22.45$.

Step3: Calculate sum of products and total frequency

$\sum_{i = 1}^{5}m_if_i=2.45 + 44.7+124.5+104.7+22.45 = 300.8$. Total frequency $n=1 + 6+10+6+1=24$.

Step4: Calculate mean

Mean $\bar{x}=\frac{\sum_{i = 1}^{5}m_if_i}{n}=\frac{300.8}{24}\approx12.53$.

Answer:

$12.53$