STATS ch 3

A​ student's course grade is based on one midterm that counts as 5​% of his final​ grade, one class project that counts as 20​% of his final​ grade, a set of homework assignments that counts as 50​% of his final​ grade, and a final exam that counts as 25​% of his final grade. His midterm score is 73​, his project score is 86​, his homework score is 78​, and his final exam score is 69. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.

(0.05)73+(0.20)86+(0.50)78+(0.25)69 = 77.1

A random sample of 10 subjects have weights with a standard deviation of 13.7134 kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result.

188.0573 kg^2 SQUARE THE SD = 13.7134^2

The following are the ratings of men by women in an experiment involving speed dating. Use the given data to construct a boxplot and identify the​ 5-number summary. 3.0 3.0 4.0 4.0 4.5 4.5 5.5 5.5 5.5 5.5 5.5 6.0 6.0 6.0 6.0 6.0 7.0 8.0 8.5 8.5

3,4.5,5.5,6,8.5

Which distribution shape​ (skewed left, skewed​ right, or​ symmetric) is most likely to result in the mean being substantially smaller than the​ median?

A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left.

For data sets having a distribution that is approximately​ bell-shaped, _______ states that about​ 68% of all data values fall within one standard deviation from the mean.

Empirical rule

If the standard deviation for a data set is​ zero, what can you conclude about the​ data?

The data values must all be equal.

​Suppose, on the warmest day of the​ month, the daily high temperature in a city is accidentally recorded as 700 instead of 70 degrees Fahrenheit. Compare the effect this mistake will have on the mean monthly high temperature to the effect on the median monthly high temperature.

The mean will increase​ significantly, but the median will not change as a result of the mistake.

Which of the following is NOT a measure of​ center?

census

The​ ___________ is found by adding all the data values and dividing by the total number of values.

mean

When an odd number of data values are arranged in​ order, the​ _________ is the middle value.

median

The value that divides a histogram into two equal areas is called the​ ____________. The value that serves as a balancing point for a histogram is the​ ____________.

median, mean

If the maximum and minimum values in a data set are​ averaged, the result is the​ __________. high+low/2

midrange

The measure of center that is the value that occurs with the greatest frequency is the​ _______.

mode

The Range Rule of Thumb roughly estimates the standard deviation of a data set as​ _______.

s= range/4

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

significantly low or significantly high

Whenever a data value is less than the​ mean, _______.

the corresponding z-score is negative

The square of the standard deviation is called the​ _______.

variance

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​ _______.

z-score The term​ z-score represents a standardized value and is the number of standard deviations that a given​ x-value is above or below the mean.

What is the symbol used to represent the population standard​ deviation?

σ

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given question. Listed below are the jersey numbers of 1111 players randomly selected from the roster of a championship sports team. What do the results tell​ us? 20 79 54 51 77 76 53 94 43 33 8 e. What do the results tell​ us?

a. 53.5 b. 53 c. there is no mode d. 51 3. The jersey numbers are nominal data and they do not measure or count​ anything, so the resulting statistics are meaningless.

Below are the jersey numbers of 11 players randomly selected from a football team. Find the​ range, variance, and standard deviation for the given sample data. What do the results tell​ us? 43 5 63 92 78 82 7 38 69 61 39

range = 87 *max-min variance Variance=(43−48.82)2+(5−48.82)2+...+(39−48.82)211 Variance = \{(43 - 48.82)^2 + (5 - 48.82)^2 +... + (39 - 48.82)^2}/11 Variance=11(43−48.82)2+(5−48.82)2+...+(39−48.82)2​ Variance≈30.51+1557.45+228.85+171.69+104.94+128.14+1521.15+110.26+357.29+115.24+98.6411Variance ≈ \frac{30.51 + 1557.45 + 228.85 + 171.69 + 104.94 + 128.14 + 1521.15 + 110.26 + 357.29 + 115.24 + 98.64} Variance≈1130.51+1557.45+228.85+171.69+104.94+128.14+1521.15+110.26+357.29+115.24+98.64​ Variance≈5352.8611≈486.62Variance ≈ \{5352.86}{11} ≈ 486.62V ariance≈5352.86/11​≈486.62 SD ROOTVariance​

What is the symbol used to represent the sample standard​ deviation?

s