Exercises for Homework 12

12.6. There are the following data on a number of industrial subdivisions on each of 100 agricultural enterprises:

2, 4, 5, 3, 4, 6, 7, 4, 5, 3, 3, 4, 2, 6, 5, 4, 7, 2, 3, 4, 4, 5, 4, 3, 4, 6, 6, 5, 2, 3, 4, 3, 5, 6, 7, 2, 4, 3, 4, 5, 4, 6, 7, 2, 5, 3, 5, 4, 3, 7, 2, 4, 3, 4, 5, 4, 3, 2, 6, 7, 6, 4, 3, 2, 3, 4, 5, 4, 3, 5, 4, 3, 2, 6, 4, 5, 7, 5, 4, 3, 4, 5, 7, 4, 3, 4, 5, 6, 5, 3, 4, 2, 2, 4, 3, 7, 5, 6, 4, 5.

Compose the series of distribution of the agricultural enterprises on number of industrial subdivisions for one economy. Find cumulative and relative frequencies. Represent the variation series graphically. Determine the average number of industrial subdivisions for one economy, the modal and median values of the number of subdivisions, the dispersion and the average quadratic deviation (economy – хозяйство).

12.7. There are the following data on an area of crops of vegetables in the economies of the set of districts.

The area of crops of vegetables on an economy

District	Number of economies
	1	2	3	4	5	6	7
1	8	10	12	6	15	30	21
2	32	16	26	41	44	38	-
3	101	165	230	144	84	76	260
4	22	30	44	18	16	31	-
5	10	7	4	3	12	7	6
6	255	366	384	273	450	510	-
7	121	84	96	110	161	143	-
8	34	16	84	71	36	8	17
9	46	41	48	52	50	58	-
10	15	24	86	144	34	14	24

Give the comparative estimation of variability of the area of crops of vegetables in the economies of two districts (variability – колеблемость; crop – посев).

12.8. Workers of an enterprise are grouped by age.

Distribution of workers of the enterprise by age

Categories of workers	Age of workers, years					Total number of workers
	Up to 30	30-40	40-50	50-60	From above 60
Workers	43	141	216	127	118	645
Heads	2	4	6	8	4	24
Specialists	3	18	30	34	22	107
Total number of workers	48	163	252	169	144	776

Determine: the average age of workers of the enterprise as a whole and on the marked categories; the modal and median values of age of workers on categories and on the enterprise; the dispersion and the average quadratic deviation of age on categories of workers and on the enterprise; the intergroup dispersion of age of workers. Find the general dispersion of age of workers by using the rule of addition of dispersions.

12.9. The administration of a supermarket is interested in the optimal level of stocks of products in a trading hall, and also the monthly average volume of purchases of the goods which are not subjects of daily consumption in a family (for example such as soda). For finding-out of this question the manager of a supermarket within January was registering the frequency of purchases of 100-gramme packages with soda and has collected the following data x_i:

4, 4, 9, 3, 3, 1, 2, 0, 4, 2, 3, 5, 7, 10, 6, 5, 7, 3, 2, 9, 8, 1, 4, 6, 5, 4, 2, 1, 0, 8

Construct the variation series, determine its numerical characteristics. Which recommendations would you give to the administration of the supermarket?

L E C T U R E 13