Unit 8: Descriptive Statistics and Time Series - Practice Quiz

1 Which measure of central tendency is calculated by dividing the sum of all observations by the number of observations?

2 What is the median of the data set ?

3 What is the mode of the data set ?

4 Which measure of central tendency is least affected by extreme values?

5 Which measure of dispersion is the difference between the largest and smallest observations?

6 What is the range of the data set ?

7 Which measure is the positive square root of variance?

8 What does a small standard deviation indicate?

9 Which distribution is symmetric and bell-shaped?

10 In a perfectly normal distribution, what is the relationship among the mean, median, and mode?

11 A distribution with a long tail extending toward higher values is called what?

12 What does a frequency distribution show?

13 What does an index number generally measure?

14 What value is commonly assigned to the base year in an index number?

15 Which index measures changes in the prices paid by consumers for a basket of goods and services?

16 If a price index rises from to , what percentage increase does it indicate?

17 What is a time series?

18 Which component of a time series represents the long-term general movement?

19 Which time series component describes patterns that repeat within a year?

20 Which method is commonly used to smooth short-term fluctuations in time series data?

21 The mean of five observations is 18. If one observation valued at 24 is replaced by 14, what is the new mean?

22 The values have a median equal to:

23 A dataset has mean 25 and median 21. Which conclusion is most reasonable about its distribution?

24 The mode of the observations is:

25 The average score of 20 students is 64, while the average score of 30 students is 72. What is the combined average score?

26 For the data , the range is:

27 Two datasets have the same mean. Dataset A has a standard deviation of 3, and Dataset B has a standard deviation of 7. Which statement is correct?

28 If every value in a dataset is increased by 10, what happens to its standard deviation?

29 A dataset has a variance of 49. Its standard deviation is:

30 The first and third quartiles of a dataset are 18 and 42, respectively. What is the interquartile range?

31 In a moderately positively skewed distribution, which relationship is generally expected?

32 A distribution has most observations concentrated near the center, with approximately equal tails on both sides. Which description best fits it?

33 For a normal distribution with mean 50 and standard deviation 10, approximately what percentage of observations lie between 40 and 60?

34 A dataset has a coefficient of skewness of . What does this indicate?

35 The price of a product increases from in the base year to in the current year. Using the simple price index method, what is the index number?

36 A consumer price index rises from 120 to 132. What is the percentage increase in the price level?

37 The prices of two commodities change as follows: Commodity A rises from 10 to 12, and Commodity B rises from 20 to 25. What is the simple aggregative price index?

38 Which index number is most appropriate when the quantities purchased by consumers change substantially between the base year and current year?

39 A company records sales of 120, 135, 150, and 165 units over four consecutive quarters. Which component of the time series is most evident?

40 Monthly ice-cream sales rise every summer and fall every winter over several years. This pattern mainly represents:

41 The reported mean of 50 observations is . Later, it is found that was recorded as , while was recorded as . What is the corrected arithmetic mean?

42 For the grouped distribution below, the median is . Find the missing frequency .

| Class | – | – | – | – | – |
|---|---:|---:|---:|---:|---:|
| Frequency | | | | | |

43 The frequencies of the classes –, –, –, –, and – are respectively . If the grouped-data mode is , what is ?

44 A vehicle covers three equal-distance segments at speeds of , , and km/h. What is its average speed over the entire journey?

45 Group A contains 30 observations with mean and population variance . Group B contains 20 observations with mean and population variance . What is the population variance of the combined 50 observations?

46 For eight observations, . What is their sample variance?

47 A variable has mean and standard deviation . A transformed variable is defined by . Which statement about their coefficients of variation is correct?

48 A dataset has first quartile and third quartile . Under the decreasing transformation , what is the interquartile range of ?

49 A population is a mixture of two subpopulations. The first has weight , mean , and variance ; the second has weight , mean , and variance . What is the variance of the mixture?

50 A distribution has raw moments about the origin , , , and . What is its coefficient of kurtosis ?

51 A normal distribution has median and interquartile range . Using , what is approximately ?

52 A distribution has standardized skewness and kurtosis coefficient . If , what are the corresponding coefficients for ?

53 For two goods, the base-period data and current-period data are: A: and ; B: and . What is Fisher's ideal price index, with the base period equal to ?

54 A forward price-index ratio is and the independently calculated reverse ratio is . Both are multiplied by the same correction factor so that the time-reversal test holds. What is the corrected forward index on a base of ?

55 The annual chain-link relatives for 2021 through 2024 are , , , and , respectively. If the 2020 index is , what is the chain-base index for 2024?

56 Between two periods, the value index is and Fisher's ideal price index is , both expressed with the base period equal to . What is Fisher's ideal quantity index?

57 A quarterly series for six consecutive quarters is . What is the centered four-quarter moving average assigned to the third quarter?

58 For six equally spaced periods, a linear trend is fitted using . If , , and , what are the trend increase per calendar period and the forecast for the next period?

59 In a ratio-to-moving-average analysis, the unadjusted quarterly seasonal relatives are , , , and . After normalization so that the four indices sum to , what is the adjusted seasonal index for the third quarter?

60 Under a multiplicative time-series model, the trend value is , the seasonal index is , the cyclical index is , and the irregular index is . What is the observed series value?