Question

Because the mean is very sensitive to extreme​ values, it is not a resistant measure of center. By deleting some low values and high​ values, the trimmed mean is more resistant. To find the​ 10% trimmed mean for a data​ set, first arrange the data in​ order, then delete the bottom​ 10% of the values and delete the top​ 10% of the​ values, then calculate the mean of the remaining values. Use the axial loads​ (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any​ outliers, then compare the​ median, mean,​ 10% trimmed​ mean, and​ 20% trimmed mean.

Because the mean is very sensitive to extreme​ values, it is not a resistant measure of center. By deleting some low values and high​ values, the trimmed mean is more resistant. To find the​ 10% trimmed mean for a data​ set, first arrange the data in​ order, then delete the bottom​ 10% of the values and delete the top​ 10% of the​ values, then calculate the mean of the remaining values. Use the axial loads​ (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any​ outliers, then compare the​ median, mean,​ 10% trimmed​ mean, and​ 20% trimmed mean.

246	261	268	274	276	279	280	284	285	285
285	288	290	291	294	295	296	299	311	503

Answer 1

Solution:

For the given data set, we have to compute the mean, median, 10% trimmed mean, and 20% trimmed mean.

First of all we have to arrange the given data in an increasing order. Data in increasing order is given as below:

No.	X
1	246
2	261
3	268
4	274
5	276
6	279
7	280
8	284
9	285
10	285
11	285
12	288
13	290
14	291
15	294
16	295
17	296
18	299
19	311
20	503
Total	5890
Mean	294.5
Median	285

For this data, we have

Total sum = ∑X = 5890

Number of observations = n = 20

Mean = ∑X/n = 5890/20 = 294.5

Median = Middle most value = average of 10^th and 11^th observation = (285 + 285) / 2 = 285

Now, we have to find 10% trimmed mean.

So, we have to remove n*10% = 20*10% = 2 observations from bottom and top of the given data.

So, we have following data:

No.	X
1	268
2	274
3	276
4	279
5	280
6	284
7	285
8	285
9	285
10	288
11	290
12	291
13	294
14	295
15	296
16	299
Total	4569
Mean	285.5625

For this data, we have

Total sum = ∑X = 4569

Number of observations = n = 16

Mean = ∑X/n = 4569/16 = 285.5625

10% trimmed mean = 285.5625

Now, we have to find the 20% trimmed mean.

So, we have to remove n*20% = 20*20% = 4 observations from bottom and top of the given data.

So, we have following data:

No.	X
1	276
2	279
3	280
4	284
5	285
6	285
7	285
8	288
9	290
10	291
11	294
12	295
Total	3432
Mean	286

For this data, we have

Total sum = ∑X = 3432

Number of observations = n = 12

Mean = ∑X/n = 3432/12 = 286

20% trimmed mean = 286