Question

Last question was inncorrectly typed:1.A sample of students who has taken a calculus test has a mean =78.2, mode =67, median 67.Based on this information, the distribution of scores is: symmetric, right skewed, left skewed, bimodal...2. the average score for a class of 35 students was 70. the 20 male student's in the class averaged 73, the 15 female student's in the class averaged: 73, 70, 66, 60So if I am this bad at the work imagine how the tests will go... ugh

Answer 1

Answer:

(A) The data set of the sample of students who has taken a calculus test is right skewed.

(B) The average of female students in the class is 66.

Step-by-step explanation:

(A)

For a left skewed distribution the Mean < Median < Mode.

For a right skewed distribution the Mean > Median > Mode.

For a symmetric distribution the Mean = Median = Mode.

Given: Mean = 78.2, Median = 67 and Mode = 67

In this case the mean of the data is more than the median and mode.

$Mean = 78.2>Median = Mode = 67$

Thus, the data set of the sample of students who has taken a calculus test is right skewed.

(B)

Total number of student ($n$) = 35

Combined average ($\mu_{c}$) = 70

Number of male student ($n_{M}$) = 20

Average of male students ($\mu_{M}$) = 73

Number of female student ($n_{F}$) = 15

Average of female students = $\mu_{F}$

The formula to compute the combined average is:

$\mu_{c}=\frac{n_{M}\mu_{M}+n_{F}\mu_{F}}{n_{M}+n_{F}}$

Compute the value of $\mu_{F}$ as follows:

$\mu_{c}=\frac{n_{M}\mu_{M}+n_{F}\mu_{F}}{n_{M}+n_{F}}\\70=\frac{(20\times73)+(15\times\mu_{F})}{20+15}\\ 70\times35=1460+(15\times\mu_{F})\\\mu_{F}=\frac{2450-1460}{15} \\=66$

Thus, the average of female students in the class is 66.