Question

a sample of college students was asked how much they spent monthly on pizza. approximate the mean for the cost.
monthly pizza cost ($)\tnumber of students
10.00 - 19.99\t9
20.00 - 29.99\t20
30.00 - 39.99\t21
40.00 - 49.99\t11
50.00 - 59.99\t5
the mean for the cost is $ (round to the nearest cent as needed.)

Explanation:

Step1: Find mid - points of each class

For 10.00 - 19.99, mid - point $x_1=\frac{10 + 19.99}{2}=14.995$; for 20.00 - 29.99, $x_2=\frac{20+29.99}{2}=24.995$; for 30.00 - 39.99, $x_3=\frac{30 + 39.99}{2}=34.995$; for 40.00 - 49.99, $x_4=\frac{40+49.99}{2}=44.995$; for 50.00 - 59.99, $x_5=\frac{50 + 59.99}{2}=54.995$.

Step2: Calculate the product of mid - points and frequencies

$f_1 = 9$, $f_1x_1=9\times14.995 = 134.955$; $f_2 = 20$, $f_2x_2=20\times24.995 = 499.9$; $f_3 = 21$, $f_3x_3=21\times34.995 = 734.895$; $f_4 = 11$, $f_4x_4=11\times44.995 = 494.945$; $f_5 = 5$, $f_5x_5=5\times54.995 = 274.975$.

Step3: Find the sum of frequencies and the sum of products

$\sum f_i=9 + 20+21+11+5=66$; $\sum f_ix_i=134.955 + 499.9+734.895+494.945+274.975 = 2149.67$.

Step4: Calculate the mean

$\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{2149.67}{66}\approx32.57$.

Answer:

$32.57$