Tests: Statistics
Click an option: a correct answer turns green, a wrong one turns red, and an explanation appears. Tests in total: 43.
Sets by topic (10 questions each)
One set is ten questions with a result at the end. Pick a topic and a set number.
A courier service recorded order delivery times (minutes) over eight days: 12, 4, 19, 7, 15, 9, 6, 14. Find the interquartile range (Q3 − Q1), calculating the quartiles as the medians of each of the two equal halves of the ordered series.
At a bank branch an operator serves 60 customers a day on average, with a standard deviation of 8 customers. Yesterday the operator served 76 customers. What is the standardized deviation (z-score) of yesterday's result?
A hypothetical district has 180,000 residents and an area of 450 square kilometres. What is the population density (a relative indicator of intensity)?
At the Baraka Tikuv sewing workshop a worker's nominal wage was 120% of last year's, while the consumer price index over the same period was 108%. What is the real wage index (to one decimal place)?
The relationship between a flower shop's weekly sales (y, million soums) and its advertising spending (x, million soums) is expressed by the paired linear regression equation y = 12 + 3x. If 5 million soums are spent on advertising, what sales does the equation predict?
Last year "Bahor mebel" sold products worth 200 mln soum. This year's plan was set at 105% of last year, and the plan was fulfilled at 104%. What is the relative dynamics indicator of sales compared with last year?
To study customers' waiting time in the queue, a post office observed 36 customers using repeated (with-replacement) random sampling. The standard deviation in the sample is 12 minutes. What is the mean sampling error of the average (σ / √n)?
The 40 workers of the "Charxpalak" sewing workshop are being divided into 4 equal-interval groups by monthly wage. The lowest wage is 3 mln soum, the highest is 11 mln soum. What will be the width of each interval?
A tea shop calculated the linear correlation coefficient between advertising spending and weekly sales: r = 0.9. What share of the variation in sales does the coefficient of determination (r²) explain as linked to advertising?
According to three years of data from the "Qorbobo" ice cream kiosk, average sales in July are 45 mln soum, while average monthly sales across all months are 30 mln soum. What is the seasonality index for July?
A city bus was late on six trips by (minutes): 4, 11, 7, 2, 15, 9. What is the range of this series?
In the current month a canteen bought 30 kg of meat (the price rose from 80 000 to 88 000 soum) and 100 kg of carrots (the price rose from 5 000 to 6 000 soum). What is the aggregate price index weighted by current-period quantities (Paasche formula: Σp1q1 / Σp0q1)?
For a confectionery workshop's sales: the price index is 108% and the physical volume (quantity) index of products sold is 125%. What is the sales value (revenue) index?
Flour stock in a bakery warehouse at the start of each month: 1 January 40 t, 1 February 44 t, 1 March 50 t, 1 April 46 t. What is the average stock for Q1 for a point-in-time series with equal intervals (chronological average)?
The "Qo'qon mexanika" plant employs 240 workers and 30 engineers. Using the relative coordination indicator, how many engineers are there per 100 workers?
Annual sales of the "Yashil vodiy" plant nursery (mln soum): 2023 – 40, 2024 – 46, 2025 – 49, 2026 – 58. What is the average annual absolute increase for this time series?
The average annual population of a hypothetical district is 250 000 people, and 5 000 children were born during the year. What is the crude birth rate (per 1 000 population, in per mille)?
Grouping of a logistics firm's drivers by length of service: 0–10 years – 4 people, 10–20 years – 10 people, 20–30 years – 6 people. Using the interval midpoints, what is the average length of service?
An ice cream workshop calculated the linear correlation coefficient from 12 weeks of price and sales volume data: r = −0.85. What is the correct interpretation of this result?
Daily deliveries of four couriers: 3, 5, 7, 9 (mean 6, variance 5 when calculated by dividing by n). The next day each courier delivered exactly 5 more: 8, 10, 12, 14. How do the mean and the variance change?