Question

mean, median, mode, range
45.6, 54.6, 44.6, 46.5, 66.4, 54.6
mean = 52.05 median = 45.1
mode = ____ range = ____
1.6, 2.2, 1.6, 3.5, 2.4, 2.2, 3.5, 2.4, 2.2
mean = ____ median = ____
mode = ____ range = ____
120, 320, 330, 220, 202, 210, 230, 320, 210, 201, 310, 330, 240, 210, 330, 230
mean = ____ median = ____
mode = ____ range = ____
54.2, 34.5, 53.4, 45.8, 24.6, 38.6, 26.8, 43.5, 45.2, 42.6
mean = ____ median = ____
mode = ____ range = ____

Explanation:

Step1: Calculate mean for first set

Mean is sum of values divided by number of values. Sum of 45.6, 54.6, 44.6, 46.5, 66.4, 54.6 is $45.6 + 54.6+44.6 + 46.5+66.4+54.6=312.3$. There are 6 values, so mean is $\frac{312.3}{6}=52.05$.

Step2: Calculate median for first set

Arrange values in ascending order: 44.6, 45.6, 46.5, 54.6, 54.6, 66.4. Since there are 6 (even) values, median is average of middle two, $\frac{46.5 + 54.6}{2}=50.55$.

Step3: Calculate mode for first set

Mode is most - frequent value. 54.6 appears twice, more frequently than others, so mode is 54.6.

Step4: Calculate range for first set

Range is difference between largest and smallest values. Range is $66.4−44.6 = 21.8$.

Step5: Calculate mean for second set

Sum of 1.6, 2.2, 1.6, 3.5, 2.4, 2.2, 3.5, 2.4, 2.2 is $1.6\times2+2.2\times4 + 3.5\times2+2.4\times2=3.2 + 8.8+7+4.8 = 23.8$. There are 9 values, so mean is $\frac{23.8}{9}\approx2.64$.

Step6: Calculate median for second set

Arrange in ascending order: 1.6, 1.6, 2.2, 2.2, 2.2, 2.2, 2.4, 2.4, 3.5, 3.5. Since there are 9 (odd) values, median is the 5th value, which is 2.2.

Step7: Calculate mode for second set

2.2 appears 4 times, more frequently than others, so mode is 2.2.

Step8: Calculate range for second set

Range is $3.5−1.6 = 1.9$.

Step9: Calculate mean for third set

Sum of 120, 320, 330, 220, 202, 210, 230, 320, 210, 201, 310, 330, 240, 210, 330, 230 is $120 + 320\times2+330\times4+220+202+210\times4+230\times3+201+310+240=120 + 640+1320+220+202+840+690+201+310+240 = 4883$. There are 16 values, so mean is $\frac{4883}{16}=305.1875$.

Step10: Calculate median for third set

Arrange in ascending order: 120, 201, 202, 210, 210, 210, 220, 230, 230, 230, 240, 310, 320, 320, 330, 330, 330, 330. Since there are 16 (even) values, median is average of 8th and 9th values, $\frac{230 + 230}{2}=230$.

Step11: Calculate mode for third set

330 appears 4 times, more frequently than others, so mode is 330.

Step12: Calculate range for third set

Range is $330−120 = 210$.

Step13: Calculate mean for fourth set

Sum of 54.2, 34.5, 53.4, 45.8, 24.6, 38.6, 26.8, 43.5, 45.2, 42.6 is $54.2+34.5+53.4+45.8+24.6+38.6+26.8+43.5+45.2+42.6 = 409.2$. There are 10 values, so mean is $\frac{409.2}{10}=40.92$.

Step14: Calculate median for fourth set

Arrange in ascending order: 24.6, 26.8, 34.5, 38.6, 42.6, 43.5, 45.2, 45.8, 53.4, 54.2. Since there are 10 (even) values, median is average of 5th and 6th values, $\frac{42.6+43.5}{2}=43.05$.

Step15: Calculate mode for fourth set

No value appears more than once, so there is no mode.

Step16: Calculate range for fourth set

Range is $54.2−24.6 = 29.6$.

Answer:

First set: Mean = 52.05, Median = 50.55, Mode = 54.6, Range = 21.8
Second set: Mean $\approx$ 2.64, Median = 2.2, Mode = 2.2, Range = 1.9
Third set: Mean = 305.1875, Median = 230, Mode = 330, Range = 210
Fourth set: Mean = 40.92, Median = 43.05, Mode = None, Range = 29.6