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18 Sep 2024, 18:54
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The years in which the Item B prices were highest were also the years for which the price index was least.: No
The prices of Item A were positively correlated with the price index.: Yes
The prices of Item C and the prices of Item D were positively correlated.: No
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
80% (01:58) correct
20%
(02:25)
wrong
based on 436
sessions
History
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Not Attempted Yet
For each of the last six years, the table shows the price, in Bangladeshi taka, of one unit for each of 4 types of items—ltems A through D. The price index shown in the table is the sum of the prices of certain numbers of units of each type of item. For instance, the price index for each year includes the cost of 20 units of Item A.
| Year | A | B | C | D | Price Index |
|---|---|---|---|---|---|
| 1 | 3 | 10 | 9 | 3 | 345 |
| 2 | 3 | 12 | 10 | 1 | 347 |
| 3 | 5 | 12 | 8 | 5 | 407 |
| 4 | 8 | 10 | 6 | 5 | 415 |
| 5 | 8 | 10 | 7 | 4 | 420 |
| 6 | 6 | 8 | 5 | 6 | 358 |
| Yes | No | |
| The years in which the Item B prices were highest were also the years for which the price index was least. | ||
| The prices of Item A were positively correlated with the price index. | ||
| The prices of Item C and the prices of Item D were positively correlated. |
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Official Answer
The years in which the Item B prices were highest were also the years for which the price index was least.: No
The prices of Item A were positively correlated with the price index.: Yes
The prices of Item C and the prices of Item D were positively correlated.: No
19 Sep 2024, 16:22
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1. The question asks us to analyze the table and check the statements to see whether they are true or false.
2. The years in which the Item B prices were highest were also the years for which the price index was least. Item B its highest price - 12 - during years 2 and 3. During this time the price index was 347 and 407, respectively. However, the two lowest years for the price index had values of 345 and 347. So, the statement is false.
3. The prices of Item A were positively correlated with the price index. Positively correlated factors are when one factor increases, the other tends to do the same and the same goes for decreasing. For years 1-5, A gradually increases and the same happens with the price index. From year 5 to 6, A decreases and the price index does the same. So, the statement is true.
4. The prices of Item C and the prices of Item D were positively correlated. We have a counter-example by considering years 1-2, for example. Here, C increases, however, D decreases. So, the statement is false.
PriceGraph1.jpg [ 21.11 KiB | Viewed 4205 times ]
PriceGraph2.jpg [ 19.56 KiB | Viewed 4132 times ]
2. The years in which the Item B prices were highest were also the years for which the price index was least. Item B its highest price - 12 - during years 2 and 3. During this time the price index was 347 and 407, respectively. However, the two lowest years for the price index had values of 345 and 347. So, the statement is false.
3. The prices of Item A were positively correlated with the price index. Positively correlated factors are when one factor increases, the other tends to do the same and the same goes for decreasing. For years 1-5, A gradually increases and the same happens with the price index. From year 5 to 6, A decreases and the price index does the same. So, the statement is true.
4. The prices of Item C and the prices of Item D were positively correlated. We have a counter-example by considering years 1-2, for example. Here, C increases, however, D decreases. So, the statement is false.
Attachment:
PriceGraph1.jpg [ 21.11 KiB | Viewed 4205 times ]
Attachment:
PriceGraph2.jpg [ 19.56 KiB | Viewed 4132 times ]
General Discussion
20 Sep 2024, 05:02
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The second bit is the challenging one for me , here's how you can tackle the correlations when its not veru obvious.
M1. If the values above the average row of first quantity are smaller than the average and if the values below the average row of first quantity are larger, then there is positive correlation. This is because the sorted dataset also has smaller values above this average row since we sorted in ascending order.
Above average values should be larger than below average.
M2. Make a scatter plot an try rough curve fitting if you get positive slope line +ve correlation if downward line negative correlation.
M1. If the values above the average row of first quantity are smaller than the average and if the values below the average row of first quantity are larger, then there is positive correlation. This is because the sorted dataset also has smaller values above this average row since we sorted in ascending order.
Above average values should be larger than below average.
M2. Make a scatter plot an try rough curve fitting if you get positive slope line +ve correlation if downward line negative correlation.
