Exam 5: Numerical Descriptive Measures

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Calculate the 2nd quintile. (Hint: 2^nd quintile is L_40.)

The annual percentage rates of return over the past 10 years for two mutual funds are as follows: Fund : 7.1 -7.4 19.7 -3.9 32.4 41.7 23.2 4.0 1.9 29.3 Fund B: 10.8 -4.1 5.1 10.9 26.5 24.0 16.9 9.4 -2.6 10.1 Which fund would you classify as having the higher level of risk?

The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately 75%.

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 165 175 150 155 173 149 145 153 153 153 152 145 164 143 170 175 148 174 171 156 166 168 152 150 173 168 146 155 172 159 Determine the location and value of the 65th percentile of the weights.

The mode is the only measure of central location for a distribution of a nominal (categorical) variable.

Chebyshev's theorem states that the percentage of observations in a data set that should fall within 3 standard deviations of their mean is at least 88.9%.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Find the lower quartile of the ages.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Construct a box plot for the age data and identify any outliers.

The least squares method is the method of deriving a linear equation between two numerical variables.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Find the upper quartile of the ages.

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 75% of deliveries take more than 4 hours?

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a mound-shaped distribution, what can we say about the proportion of ratios that fall between: a. 11.5 and 15.5? b. 9.5 and 17.5? c. 7.5 and 19.5?

The correlation coefficient only measures the direction and strength of a linear relationship between two numerical variables.

The left side of the box in a boxplot is the first quartile and the right side of the box in a boxplot is the third quartile, so the width of the box is the interquartile range.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Compute the 8th decile of the data.

Data were obtained for the weight in grams, of a sample of 10 packets of sweetener, as found in cafés. 4.5 5 5.9 5.4 5.5 4.7 4.9 4.7 4.7 4.6 Find the mean, median and mode weight packet of sweetener and explain which is best measure of central location.

In a positively skewed distribution, the mean is larger than the median and the median is larger than the mode.

When is the standard deviation of a data set smaller than its variance? Explain.

While Chebyshev's theorem applies to any distribution, regardless of shape, the empirical rule applies only to distributions that are bell-shaped and symmetrical.

The difference between the largest and smallest values in an ordered array is called the range.