141, 330, 292, 198, 263, 224, 149, 121, 223, 125, 126, 48, 111, 327, 238
mean
median
mode
range
mad
and box in whiskers
mean = 190.73
median = 223
mode = There is no mode as no number repeats.
range = 282
mad = 82.19
Box and whisker plot:
| |
____|_______|_______
| |
48 | 121 | 141
| |
149 | 198 | 223
| |
224 | 238 | 263
| |
292 | 327 |
| |
The box and whisker plot shows the minimum and maximum values, the lower and upper quartiles, and the median. The boxes show the interquartile range (IQR), which is the range between the first and third quartiles. The line in the middle of the box represents the median, the lower end of the box represents the first quartile, and the upper end of the box represents the third quartile. The whiskers show the range from the minimum to the first quartile and from the third quartile to the maximum. The dots outside the whiskers represent the outliers.
and what is the mad
The MAD stands for Mean Absolute Deviation, which is a measure of the variability of the data. To calculate the MAD, we take the absolute value of the distance between each data point and the mean of the data set. Then, we take the average of these absolute deviations.
To calculate the MAD for this data set, we would follow these steps:
1. Calculate the mean of the data set:
mean = (141 + 330 + 292 + 198 + 263 + 224 + 149 + 121 + 223 + 125 + 126 + 48 + 111 + 327 + 238) / 15
= 190.73
2. Calculate the absolute deviation from the mean for each data point:
|141 - 190.73| = 49.73
|330 - 190.73| = 139.27
|292 - 190.73| = 101.27
|198 - 190.73| = 7.27
|263 - 190.73| = 72.27
|224 - 190.73| = 33.27
|149 - 190.73| = 41.73
|121 - 190.73| = 69.73
|223 - 190.73| = 32.27
|125 - 190.73| = 65.73
|126 - 190.73| = 64.73
|48 - 190.73| = 142.73
|111 - 190.73| = 79.73
|327 - 190.73| = 136.27
|238 - 190.73| = 47.27
3. Calculate the average of the absolute deviations:
MAD = (49.73 + 139.27 + 101.27 + 7.27 + 72.27 + 33.27 + 41.73 + 69.73 + 32.27 + 65.73 + 64.73 + 142.73 + 79.73 + 136.27 + 47.27) / 15
= 82.19
So the MAD of this data set is 82.19.
you were wrong.
I apologize for any incorrect information I may have provided. Please let me know specifically what was incorrect so I can correct my mistake and provide the correct information.
To calculate the mean, median, mode, range, and MAD (Mean Absolute Deviation) of the given set of numbers, you can follow these steps:
Step 1: Sort the numbers in ascending order.
48, 111, 121, 125, 126, 141, 149, 198, 223, 224, 238, 263, 292, 327, 330
Step 2: Calculate the mean.
Mean = sum of all the numbers / total count of numbers
Mean = (48 + 111 + 121 + 125 + 126 + 141 + 149 + 198 + 223 + 224 + 238 + 263 + 292 + 327 + 330) / 15
Mean ≈ 198.27
Step 3: Calculate the median.
Median is the middle value when the numbers are arranged in ascending order. For this set of numbers, since there are 15 numbers, the median would be the 8th value.
Median = 149
Step 4: Calculate the mode.
Mode is the value that appears most frequently in the set of numbers.
In this case, there is no value that appears more than once, so there is no mode.
Step 5: Calculate the range.
Range is the difference between the highest and lowest value in the set.
Range = 330 - 48 = 282
Step 6: Calculate the MAD (Mean Absolute Deviation).
MAD is the average of the absolute differences between each value and the mean.
|MAD| = (|48 - 198.27| + |111 - 198.27| + |121 - 198.27| + ... + |327 - 198.27| + |238 - 198.27|) / 15
|MAD| ≈ 73.43
Finally, for "box and whiskers," we need to create a box plot diagram. This diagram visually represents the distribution of the dataset, including the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. However, since it requires graphing, I won't be able to show it here. You can use software or online tools to create a box plot for the given set of numbers.